Thermal and high-pressure [4 2] cycloadditions of buta-1,3-diene (3), cyclohexa-1,3-diene (5), and 2,3-dimethylbuta-1,3-diene (6) to alkyl glyoxylates of type 2 ( R n-Bu, i-Pr, t-Bu), catalyzed by chromium complex (R,R)-1, leading to the corresponding cycloadducts 4, 7 and 8 with relatively high enantioselectivity, are described.